help-23

[untold charm]

0.825

0.625

[noble mango]

Good!

So

what's 5 + 5/8?

[untold charm]

5.625

[noble mango]

Perfect!

Okay good

Now

Which of these numbers is the biggest?

[untold charm]

ok time to line it up

[noble mango]

Exactly :D

[untold charm]

5.625

[noble mango]

mmmm

What's the smallest out of all of these numbers?

[untold charm]

5.7

[noble mango]

are you sure

Hmmmm

Wait

[untold charm]

no it 5.667

[noble mango]

Let me ask you a question

Which one is the smallest number in the following:

5700, 5600, 5625 and 5667

[untold charm]

5600

[noble mango]

Good!

So

Which one is the smallest here:

5.7, 5.6, 5.625 and 5.667?

[untold charm]

5.6

[noble mango]

Amazing! Yes

That's right

5.6 is the smallest number

[untold charm]

do i add it from the start

[noble mango]

Yeah

5.6 goes at the start

Because its lowest to highest

[untold charm]

ok then 5.7 goes next

hellooo

[noble mango]

Wait

Let's go back to my example

5700, 5600, 5625, 5667

We know the smallest number is 5600, right?

What's the next smallest number?

[untold charm]

yup

5625

[noble mango]

Good! So

5.7, 5.6, 5.625, 5.667

The smallest number is 5.6. What is the next smallest number?

[untold charm]

5.667

[noble mango]

mmmmmmmmmmmmmmmmmmmmm are you sure?

Your previous answer seems to disagree

[untold charm]

oh

[noble mango]

Don't think too hard :)

[noble mango]

The next smallest number is this

[noble mango]

So

What do you think

The next smallest number here is?

[untold charm]

5.7

[noble mango]

It's not a trick question, I assure you

[noble mango]

nope

[formal mountain]

isnt 5.625

[noble mango]

[formal mountain]

5.625>5.6

[noble mango]

If the smallest number is 5.6, the next smallest is 5.625

[untold charm]

https://tenor.com/view/kill-me-shoot-me-kms-shoot-choking-gif-18076903094489133625

it 5.625

[noble mango]

yep

[formal mountain]

the smallest number in the chain of answers to choose from is 100% 5.6, 5.6 = 5.600

just put all the numbers in the same format and choose the smallest

you shouldnt overthink it

[untold charm]

do i put it next to 5.6

[noble mango]

yes

[formal mountain]

yes

5.600, 5.625, 5.667, 5.700

from small to big little to high however u want to call it

[untold charm]

ok then after that is 5.7

[formal mountain]

no

after 5.625 = 5.667

[untold charm]

oh so it 5.667

[formal mountain]

yes

5.600 < 5.625 < 5.667 < 5.700

[untold charm]

the last one is 5.7

[formal mountain]

yep

[untold charm]

ok next one i have a back side to

[formal mountain]

are you allowed to use a calculator

would make it easier on your behalf i think

[untold charm]

the backside yes

here it is

[formal mountain]

alright

so

lets say u have 5/10th

right

thats the same as 0.5

[untold charm]

were on number 8

[formal mountain]

the correct mathematical way to give an answer in this context is giving the tiniest fraction

[formal mountain]

im giving an example

an explanation

[untold charm]

oh

[formal mountain]

5/10th is the same as 1/2nd

1/6th would be the same as 2/12th

1/6th is just the shortened version of 2/12th

u have to have some sort of insight to get the answer for equations like this

[untold charm]

ok

[formal mountain]

i recommend u watch strategy videos on youtube if youre really struggling, or read the provided theory

[untold charm]

ok

im on 9

question 9

its 2/?

[formal mountain]

2/3

[exotic niche]

Aight hello guys

[formal mountain]

👋

[untold charm]

im on the back now we can use calculators

[formal mountain]

okay

good luck :p

[untold charm]

ok

i might need help

[exotic niche]

Send picture of the back, or is it further up

[untold charm]

cause i kinda know how to use a calculator

[exotic niche]

Kinda blurry

[exotic niche]

Kinda cut off --

Sorry for being so annoying lol

[untold charm]

no its fine

[exotic niche]

Aight that's fine

[untold charm]

ok

[exotic niche]

Is this like hw or a practice exam or smthn

[untold charm]

nah it homework due ||tomorrow||

[exotic niche]

Cold

[untold charm]

...

[exotic niche]

Aight go ahead and start

Is this part calc

[untold charm]

ok

0.625 for the first one

[exotic niche]

Ya

[untold charm]

4/5 is 0.8

[exotic niche]

Ya

[untold charm]

o.8 goes first

0.8

[exotic niche]

Waig

[exotic niche]

Have u converted eveyrthjng

[untold charm]

yes

[exotic niche]

K list them out in the order u think they should go

Ascending

[untold charm]

0.625 0.8 0.08 0.875 and 8

[exotic niche]

Aight, first make them all have the same number of decimal places

[untold charm]

ok

[exotic niche]

0.625, 0.800, 0.080, 0.875 and 8.000

U can tell 8 is the highest so put that at the top

[untold charm]

so at he end

[exotic niche]

Yes

Then remove the 0. From all the others

[untold charm]

???

[exotic niche]

So 625, 800, 080, 875

Instead of 0.625 it's 625

[untold charm]

ok

[faint swift]

are you allowed a calculator

[untold charm]

yes

[exotic niche]

We already calculated the values

[faint swift]

Okay

[exotic niche]

So rearrange the new numbers in ascending order

The ones without the 0.

[untold charm]

0.08 turns into a 8

[exotic niche]

No remember 0.08 is equal to 0.080

So remove 0.

To get 080

[untold charm]

80

[exotic niche]

Yeh

Essentially

Now order the numbers

[untold charm]

0.8

8

0.08 at the start

??

[exotic niche]

From this set of numbers arrange them in order

[untold charm]

625 at the start

[exotic niche]

No

80 is smaller

[untold charm]

0.08 at the start

???

[exotic niche]

Right now I dont want you to focus on the decimal points just those numbers

Order th3se numbers without the decimal points in ascending order

[untold charm]

now 0.8 in front of 0.08

[exotic niche]

0.08 is smaller than 0.8

Like 80 is smaller than 800

[untold charm]

oh

[exotic niche]

Continue after 0.08

[untold charm]

875

[exotic niche]

But isn't 625 smaller than 875

So wouldn't it go before

[untold charm]

625

[exotic niche]

Then?

[untold charm]

0.8

or 0.875

[exotic niche]

Yes

[untold charm]

0.8

[exotic niche]

800 is smaller than 875

So 0.8 goes forst

[untold charm]

oh cuz i have 0.08 0.625

[exotic niche]

Now u have 0.08, 0.625, 0.8, what goes next

[untold charm]

875

[exotic niche]

Convert that to the decimal form by adding 0.

[untold charm]

0.875

[exotic niche]

Add that to ur list

What do u have

[untold charm]

0.08 0.625 0.8 0.875 8

[faint swift]

The way to think about decimal sizes is this:
When you have a decimal, the more zeros there are in the front, the smaller it is.
.01 is bigger than .001
In any example like the one you are doing, you can go break the problem up into groups in your head.
So .08 is smallest group, then .625 and .8 and .875.
Since .08 is the smallest, thats obviously first.
Then, for the next group, 6 is smaller than 8 so .625 is the next smallest.
Then, the next 2 both have 8 so we go to the next number in the decimal. The first is .80 and the other is .87. .87 is larger than .8

[untold charm]

ok im done

[exotic niche]

But remember one of em was a fraction

So convert it back

[untold charm]

done next one

[exotic niche]

K convert them into decimals

With calc

[untold charm]

i did

[exotic niche]

What's the list

[untold charm]

0.08 5/8 4/5 0.875 8

[exotic niche]

Nice

Next question?

[untold charm]

1 3/4 is 1.75

[exotic niche]

Ya

[untold charm]

got my answers

[exotic niche]

What are they

[untold charm]

1.708 is at the begeting

hi

bruh

[exotic niche]

Ye

No

[untold charm]

oh

[exotic niche]

Why would it be at the beginning

[exotic niche]

Oh what

[untold charm]

greatest to least

[exotic niche]

Isn't 1.9 greater

Remember 900 greater than 708

[untold charm]

ok

[exotic niche]

Using that logic what is next

[untold charm]

the beggeding is 1.7

[exotic niche]

I thought It is from greatest to smallets

[untold charm]

yeah

it is

[exotic niche]

But isn't there something greater than 1.7

[untold charm]

idk how to do this

[exotic niche]

Did u convert all the numbers to decimals?

If u did list them here

[untold charm]

no im still tryna figuer it out

[exotic niche]

Ok tell me when u are fully stuck

[untold charm]

im stuck

[exotic niche]

Aight, first convert all the numbers into decimals with ur calculator

List them out here

[untold charm]

how

[exotic niche]

You know that 17 over 10 is 1.7

Convert 1 and 3/4 into a mixed number

[untold charm]

ok

so 1.9 is at the beggiding

[exotic niche]

Yep

[untold charm]

then 1.7 infront of 1.9

[exotic niche]

But what's bigger than 1.7

[untold charm]

1.708

[exotic niche]

Yes and?

Another thing

[untold charm]

do i add it infront of the 1.9

[exotic niche]

There is smth. Else bigger than 1.708

Look closely at the fractions

[untold charm]

1.655 infront of the 1.9

[exotic niche]

Nono

U were on the right path

1.708 is bigger than 1.7

But what's bigger than 1.708?

[untold charm]

idk

[exotic niche]

What decinal does the 1 and 3/4 make

[untold charm]

idk

it 6:54

[exotic niche]

?

[untold charm]

in minnesota

[exotic niche]

Ok

But we needa finish this problem

[untold charm]

ok

[exotic niche]

1 and 3/4 = 7/4

What is 7/4 as a decimal

Put it in ur calculator

[untold charm]

1.75

[exotic niche]

Yes what is bigger 1.75 or 1.708

[untold charm]

1.75

do i put it infront of 1.9

[exotic niche]

Yes good

[exotic niche]

Now what is bigger 1.708 or 1.7?

[untold charm]

1.7

[exotic niche]

No 1.7 is equal to 1.700 which is smaller than 1.708

Think of it as 1700 being smaller than 1708

[untold charm]

oh it 1.708

[exotic niche]

Yes so the order goes 1.9, 1.75, 1.708, then what?

[untold charm]

then 1.655

or 1.7

[exotic niche]

Whats bigger 1.700 or 1.655

[untold charm]

1.700

[exotic niche]

So put 1.7 after 1.708

Then put 1.655

There. You go

[untold charm]

can you put it in a order

[exotic niche]

1.9, 1 and 3/4, 1.708, 17/10, 1.655

[untold charm]

ok i think i have it have a good day

.close

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[exotic niche]

Aight

[safe radish]

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[placid summit]

Hello

[magic junco]

hi

[quiet plume]

Hi!

[placid summit]

Alight my gf has a project and needs help

[magic junco]

Might want her to ask herself?

[placid summit]

Hol up then

She here

Help me

She need help with version a

.close

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[sinful thicket]

how do i solve this problem?

[sinful thicket]

do i take the inverse of f(x) or inverse of f'(x) ?

[warm warren]

$(f^{-1})^'$ is the derivative of $f^{-1}$. $(f^')^{-1}$ is the inverse of $f^'$

[flat frigate]

Annie Maqionde
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[sinful thicket]

oh i will find the inverse of f which is the original then i should find the derivative of it

[warm warren]

yes

[sinful thicket]

hmm for this f(x) how do i find the inverse for cubic

so will this be my inverse of f

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[tardy crescent]

are some cases with shell/disk method impossible

[tardy crescent]

like how would you shell method this

i see how to disk method im pretty sure

but shell looks extremely impractical if not imposible

[queen ingot]

which axis are you rotating around?

[safe radish]

@tardy crescent Has your question been resolved?

[split kayak]

$\int_a^b f(x) dx = \int_a^c f(x) dx + \int_c^b f(x) dx$

[split kayak]

not really needed since the f(x) is squared, but it might help

[tardy crescent]

uhh x axis mb

i wate dinner and came back

i think its impossible for a normal hs student cuz like

[split kayak]

whats the function like?

[tardy crescent]

for shell we wanna make it parrele to axis of rotation

[tardy crescent]

^

i cant think of a way to find the distance betwen the curves of the same function, esp since i have no idea how to break up a wuadeatoc

[split kayak]

more like, the formula

[tardy crescent]

quadratic

i guess

[queen ingot]

it looks like a cubic

[tardy crescent]

cubic mb

2x^2-x^3

[queen ingot]

you know how you get +/- in the quadratic formula?

[tardy crescent]

yeah with quad formula i suppose

[queen ingot]

there can be a situation like that here

that's why we can get two formulas

[tardy crescent]

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[supple locust]

I have a question regarding the Second Fundamental Theorem of Calculus. The formula is f(x) = d/dx [ ∫ f(t)dt ] with bounds of x and a, where a is a constant. Can we move the d/dx to the other side, such that f'(x) = [ ∫ f(t)dt ] ?

[severe pond]

yes this is just notation

[supple locust]

Thank you. Just wanted to make sure.

[severe pond]

wait

F(x) = d/dx int?

or F(x) = int

[supple locust]

Oh, sorry to cause any confusion.

Lemme rewrite that.

[severe pond]

i think you meant F'(x) = d/dx (int)?

[supple locust]

That's not what it says in my notes, which I will take a picture of shortly.

It might have been a mistake on my part.

[severe pond]

well if you have f(x) = d/dx int f then f'(x) = d^2/dx^2 int f which is not int f

[supple locust]

Sorry to interrupt, but firstly, is this the correct formula?

[severe pond]

,rotate

[severe pond]

yes this is true

but no you are confusing notation then

if you think you can just "move the d/dx" over

[supple locust]

Okay.

I thought it was what you were supposed to do in a practice problem, but I was mistaken.

Alright, I think that'll be all. Thank you for your help!

.close

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[last trellis]

this is DATA MANAGMENT math

How does he go from -1.84 TO 0.0329?????

Like what

[jolly sail]

look it up in the z-table

[last trellis]

ik but idk if he will give me it

i have a test on it tomorrow

[jolly sail]

bruh he must give it, theres no way teacher gonna twll u to memorize allat

[last trellis]

idk if he will give us a z table during the test or not

[last trellis]

is there a way to calculate or na

[jolly sail]

um sorry I forgot 😅

[last trellis]

im just gonna risk it and see if he does or not ngl

frick him if he dont

thanks @jolly sail !

[potent plinth]

wait for a helper @last trellis

[last trellis]

ok

[jolly sail]

u know, why not ask ur teacher instead if the table will be given or nah

[last trellis]

he wont respond

its 1 am

and the test is today

[jolly sail]

good luck 🫡

[last trellis]

just talked to a classmate

he said yea the z score

[last trellis]

yo yk when to use a Z score formula like this ^^ when getting word problems?

like what keywords or phrases in a question will tell me to use this?

[jolly sail]

iirc thats when u want to normallize the distribution

so actually u can tell that sigma (Standard Deviation) is 12.6

and sample mean is 308

[jolly sail]

like the P(x < 170) I assume its not normalized, thats why it is changed and normalized to P(z < -1.84)

[jolly sail]

bro u have it here already, why u still ask 😭

[safe radish]

@last trellis Has your question been resolved?

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✅ Original question: #help-23 message

@last trellis Has your question been resolved?

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[untold grotto]

I'm currently struggling with a problem, how to solve for x, in 244=400/(1+350e^-0.6x)?

[peak estuary]

how would you solve 244=400/(1+350y) for y?

[quasi bison]

$\frac{400}{1+350e^{-0.6x}}=244$

this is your equation, right? @untold grotto

[peak estuary]

244 not 200

[quasi bison]

ouch

[flat frigate]

Ann

[quasi bison]

fixed that

[untold grotto]

yes, that is the equation

[quasi bison]

ok

then i will second dena's question

[untold grotto]

try to isolate y

[quasi bison]

so go and do that

[untold grotto]

isolate y or x?

[peak estuary]

y

[untold grotto]

how would I cancel out the 400

or move it

to the other side

[peak estuary]

you dont need to

your first step should be to get the y out of the denom

[untold grotto]

multiply with y on both sides?

[peak estuary]

no

multiply with 1+350y on both sides

[untold grotto]

is it supposed to look like this

[peak estuary]

can you take over, gtg. thanks

[noble mango]

Yeah but what happened to the 1 + 350y?

On the first step you had:
(1 + 350y)244 = 400
Then, you divided both sides by 244;
But somehow, the 1 disappeared from the left hand side.

[untold grotto]

I multiplied the 1 with 244

should I keep the one

[noble mango]

Yes because the 244 is already outside the brackets.

Like, it is 244 times (1 + 350y) = 400

So if you want to get rid of 244 first, you have to leave the inside of the brackets alone.

[untold grotto]

okay

I put the 1+ back

[noble mango]

Nice. What do you have now?

[untold grotto]

1+350y=400/244

[noble mango]

Good!

What would be our next step?

[untold grotto]

subtracting 1 from both sides

[noble mango]

Perfect.

[untold grotto]

if I divide again by 350 won't it give me a crazy decimal

[noble mango]

Indeed, but here's the thing.

[noble mango]

In the original question, there was e^(-0.6x) in place of y.

So, once you figure out what y is, you then substitute the e back into the equation.

That is, since you know that y = this,
That means that e^(-0.6x) = this
As well.

[untold grotto]

do I change the e to ln and put ln on the other side

[noble mango]

Elaborate

[untold grotto]

-0.6x=ln(400/244-1)/350

[noble mango]

Yep! But the 350 has to be inside the natural log too

Because you should have gotten that y = (400/244 - 1)/350

So when you replace y with e^(-0.6x), you take the natural log of the entire thing.

[untold grotto]

where would the 350 be visually then

[noble mango]

Would you agree that: [ y=\frac{\frac{400}{244}-1}{350} ]

[flat frigate]

Redfern Station

[untold grotto]

yes

[noble mango]

So when you replace $y$ with $e^{-0.6x}$, you get: [ e^{-0.6x}=\frac{\frac{400}{244}-1}{350} ] Agreed?

[flat frigate]

Redfern Station

[untold grotto]

yes

[noble mango]

Then when you take the natural log of both sides, you get:
[ -0.6x=\ln\left(\frac{\frac{400}{244}-1}{350}\right) ]

[flat frigate]

Redfern Station

[untold grotto]

yes

[noble mango]

Well yeah that's it

That's where the 350 is

[untold grotto]

then I divide with -0.06 again

[untold grotto]

thank you

[noble mango]

Exactly.

[untold grotto]

thank you so much

[noble mango]

My pleasure :)

[untold grotto]

.close

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[lone void]

is what i did correct

and do i have to do trial and error from here?

oh it says atleast 3 successful hits..

my bad

.close

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[winged flare]

lord thats scary

[lone void]

nono its pretty easy

gets done in 1 step

[winged flare]

i know

but like

trial and error

[lone void]

oh yes that part sucks

and numbers go as high as n=11

[winged flare]

no the answer is 6

[lone void]

not in this case

i meant in general

[winged flare]

they cant be THAT merciless

[lone void]

💀💀

[safe radish]

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[spiral saddle]

how to solve for theta

[hidden gyro]

from either the unit circle, or the sin inverse but then from sin inverse your theta might not be in the range of
0 < theta < 2pi

[fathom jewel]

i would recommend u to learn some standard values

[clever gale]

Grab the unit circle, we know that sin corresponds to the y-value.

We want the angle(s) on the unit circle traversed clockwise from the point (0, 1) such that the y-value is -1. Hence, we get 3π/2 radians (or 270 degrees).

Don't forget the unit circle is 2π-periodic, you can add 2π radians and it'll end up at the same value. So our general solution is θ = 3π/2 + 2πk, where k is an integer

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[past birch]

when doing Q(sqrt2)(i) and Q(i)(sqrt2) am i doing {a+bi: a,b in Qsqrt(2)} in Q(sqrt2)(i), and {a+bsqrt2: a,b in Q(i)}? thanks

[past birch]

(which are both the same but im concerned about the order of operations)

[kind seal]

Hello, would you mind latexing it or uploading a picture

It seems very confusing in text

[past birch]

ok

i wanna confirm if its true

[safe radish]

@past birch Has your question been resolved?

[hazy relic]

adjoining i gives a degree 2 extension, adjoining √2 also gives degree-2. They are independent over Q . Final field has basis 1 , i , √2 , i√2

Q(√2)(i) = Q(i)(√2)

[past birch]

yep

but i just wanna know if this is true lol

[hazy relic]

Yes

[past birch]

Thx

.close

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[opal saffron]

I'm kinda confused about this.. Is the answer just x=y and y=x?

[short jewel]

Well they're the same yes

It's a special triangle riight?

45-45-90

[opal saffron]

Oh wait

I get it

[short jewel]

What are the measurements for the legs for that type of triangle?

[opal saffron]

Thanks

There aren't any measurements

So it's js x=y, y=x

[short jewel]

Well if that's what it's asking so yes

What's the instruction though?

[opal saffron]

Thanks

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[empty trench]

what is x for 0 = sin(πx-1/4π) * cos(πx) with domain [0, 2]

[empty trench]

im stuck cause i know how i would do it normally

but idk what to do rn

[split fulcrum]

perimeter?

[empty trench]

id what its called

in english

[split fulcrum]

domain

[empty trench]

yeah domain

well uhh

how do i solve it

[split fulcrum]

do you mean 2pi not just 2?

[empty trench]

no i mean 2

it says 2

i thought 2π first too lol

if it was only sin(πx-1/4π) i could do it fine

[split fulcrum]

just do the same thing as u did with sin term

if a*b = 0 then either a=0 or b=0 so set the cos = 0 as well

[empty trench]

so i just do sin(πx-1/4π) = 0 and cos(πx) = 0?

ohhh i geti t

[split fulcrum]

Yes

[empty trench]

yeah let me try that

yeah it works

you can close it

thanks

[split fulcrum]

just type .close

[empty trench]

oh okay

.close

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[timid token]

which is better to use? im putting in an x and y value to see if its equals 1 i prefer the one with? but ai says the other one

[timid token]

it should be <=>

i think

[warm warren]

second one is objectively way easier to understand

you need not put the $\stackrel{?}{=}$ ever single time

[flat frigate]

Annie Maqionde

[timid token]

yeah okay, i will go with the second one then

ty

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[minor meadow]

Can someone please explain what the hell happened here?

[minor meadow]

It's d/dx X^x btw.

[lean otter]

Let x^x = y.

Take ln on both sides.

xlnx =lny.

Now apply chain rule.

[minor meadow]

Yeah, I also figured out how to do that. But it gives me a different result than the one that my professor did, do you know what they did on my notebook?

[lean otter]

Uhh yeah, I dunno what's going on in the notebook.

[minor meadow]

Rlly?

Idk how they solved it, it's not the same result that it gave me with the chain rule, I wanted to figure out how they solved it...

[safe radish]

@minor meadow Has your question been resolved?

[safe radish]

@minor meadow Has your question been resolved?

[minor meadow]

[safe radish]

@minor meadow Has your question been resolved?

[minor meadow]

[gusty pasture]

What exactly is your question?

[minor meadow]

#help-23 message

[gusty pasture]

Because from what I can see they just used that $x^x=e^{x\ln{x}}$ and derivate that using the rule for exponentials

[flat frigate]

KonoEmllikDa

[minor meadow]

I see, can you explain me why x^x = x^xLnx?

[gusty pasture]

Firstly it's $x^x=e^{x\ln{x}}$, this is because let's say you have a positive number $a$, since the ln is the inverse of the exponential you can write it as $e^{\ln{a}}$, so you can write $x^x=e^{\ln{x^x}}$. But the $\ln{x^x}=x\ln{x}$, so $x^x=e^{x\ln{x}}$

[flat frigate]

KonoEmllikDa

[gusty pasture]

If you don't know the rules for logarithms it is a good exercise to try to finding them using the properties of the exponential

[minor meadow]

I want to understand this but I barely do it... Hahaha

Which logaritm rule is this one? 😓

[gusty pasture]

Don't worry I think my english was really poor in that explanation. Which rule? The one where I write $a=e^{\ln{a}}$ or $\ln{x^x}=x\ln{x}$?

[flat frigate]

KonoEmllikDa

[minor meadow]

Like, this part.

Also, no worries. Your English is really good. 😅

I know that if we have e ^ x = y, ln(y) = x. But I can't understand how x^x = xlnx. 😭

[gusty pasture]

It might not be the best proof but you can start with something like this: Let's say there is a $c$ such that $\ln{a^n}=c$, then $a^n=e^c$. Given this equation, can you find a way to find an expression for $\ln{a}$?

[flat frigate]

KonoEmllikDa

[minor meadow]

I can't find it, I'm pretty new to the logaritms tbh... Can you explain it please?

I need to go rn, I'll come back in a few hours and this post will be probably closed, but I'll try to open another one just to confirm one last thing, I'm finding at least 3 ways to derivate it, but rn I'm stuck at this part, I really appreciate your help and explanation.

[gusty pasture]

I can give it to you right now, $a^n=e^c$ so $a=e^{c/n}$ therefore $\ln{a}=c/n$ or simply $\ln{a^n}=c=n\ln{a}$

[flat frigate]

KonoEmllikDa

[minor meadow]

I see, so this is the exact case with X^x, right?

But in this case we have a, e, c and n. On X^x only x and e.

Right, so X^x = xln x.

[gusty pasture]

The c should still be there when you do the x^x, because by definition you should have that c=ln(x^x), but other than that that's correct

You just need to remember that ln(a^n)=n ln(a), if you can't remember you can imagine that n is a natural number, for example say that n=3, then ln(a^3)=ln(a * a * a)=ln(a)+ln(a)+ln(a)=3ln(a). So the formula for any n should be ln(a^n)=n ln(a)

[safe radish]

@minor meadow Has your question been resolved?

[minor meadow]

@gusty pasture Somehow I got it now, it's for the theory part, can you help me to solve it in 2 different ways?

The first one is by doing the x^x = e^xlnx thing + rule of potentials, the second one is via a formula.

[gusty pasture]

Are you talking about this formula? I don't have much time, but I think I can help with it

[minor meadow]

Exactly, that formula, that's the second one.

[gusty pasture]

Do you have any idea how to do it or do you want a hint?

[minor meadow]

Give me 1 minute, I'm making it on my notebook rn.

@gusty pasture Got it... somehow.

I'm pretty sure that I'm wrong. lol

[gusty pasture]

Can you show your work so I can check it?

[gusty pasture]

yeah that's it

[minor meadow]

Oh, so that's correct?

[gusty pasture]

yes

[minor meadow]

Is there anything else I can do?

Like, move up some things to make it look better.

Or short it, idk.

[gusty pasture]

The only thing you could do is the multiplication x*x^(x-1)=x^x

Other than that, if you have the formula it's pretty straightforward

If you want to do a little bit of extra work you could derive the formula

[minor meadow]

Wait, is there something I can do so it looks like this?

Because this is the result of me doing with the chain rule...

[gusty pasture]

Sure, you just need to factorize x^x in the expression you got

[minor meadow]

WAIT

Yoo 😭 😭

I'll do by myself the other one, thank you so much dude, I really appreciate it. @gusty pasture

[gusty pasture]

No problem, I got to go now so good luck with it

[minor meadow]

Have a great day, take care!

.close

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[lapis token]

My current problem wants me to figure out w_M_z [phi]
w is an alternative basis for y and z is an alternative basis for x

Here’s the photo again

[safe radish]

@lapis token Has your question been resolved?

[safe radish]

@lapis token Has your question been resolved?

[zenith jackal]

Do you have an english version of the question lol

[lapis token]

That’s the script

I was hoping the notation would help with the relevant parts

[zenith jackal]

Ok I got it

I put the img in chatgpt told to translate

xd

[lapis token]

M,N are natural numbers and X,Y are vector spaces with the following basis:
X= {x} and Y ={y}
W is an alternative basis for X and Z is the same thing for Y
Then there are a few transformations that belong to those

And for every linear map this statement is true:

[lapis token]

Oh ok I didn’t see
I gave you a messed up translation with missing notation

[zenith jackal]

So this is what you are working on?

[lapis token]

Yes

[zenith jackal]

Okay so do you know anything of what is going on for it so you can actually solve it?
Your first step would be to build the COB matrix for the domain\

[lapis token]

Sorry I’m distracted
It’s 4am and I need to write everything on paper again after doing it because my prof forces everyone to submit handwritten notes in a mailbox

[lapis token]

Sounds like dark magic

[zenith jackal]

😭

Okay

lets simplify this

bc it looks like dark magic on paper also

[lapis token]

Im listening

I can tell you my thoughts so far tho

[zenith jackal]

go ahead

[lapis token]

Because it seemed mostly simple at first

There’s a matrix w_M_z

It either goes from z to w or from w to z

Depending on how the notation works

Because I don’t know

Welp

[zenith jackal]

To build the matrix

Take each new basis vector
Write it using the old basis of 𝑋
Put those coordinate columns next to each other.

That’s it.

[lapis token]

Since those are results of transformations I’ll have to apply them in the right order to get from w to z or vice versa

[zenith jackal]

Make sense?

$$
\Xi = [, z_1 ; z_2 ; \cdots ; z_n ,]_{X}
$$

[flat frigate]

zedias

[zenith jackal]

Look correct?

[lapis token]

Hold on

I’ll make your life easier

[zenith jackal]

so once again

back to step 1

[zenith jackal]

$$
{}{W}M{Z}[\Phi].
$$

[flat frigate]

zedias

[zenith jackal]

@lapis token do you know what each of those are?

[lapis token]

w is a basis for Y and z is a basis for X

Just like y and x

[zenith jackal]

technical terms

domain basis = 𝑍

codomain basis = 𝑊

linear map = Φ

[lapis token]

I’ve heard Domain and codomain before but I’m not too familiar with what they are

Mostly in relation to images etc

[zenith jackal]

A linear map takes vectors from one vector space (the domain) and outputs vectors in another vector space (the codomain).

The domain is where inputs live.
The codomain is where outputs live.

$$
\text{The domain of } \Phi : X \to Y \text{ is } X.
$$

[flat frigate]

zedias

[lapis token]

Alright

[zenith jackal]

This means every vector you plug into Φ comes from 𝑋.

[lapis token]

So we’re going from z to w

[zenith jackal]

are you getting me

yes

[lapis token]

Yes

And ends up in Y

But the function phi is for x->y only isn’t it
Does that mean I need to use transformations to turn z into x, x into y and y into w?

To get from z to w?

[zenith jackal]

YES

YOU GOT IT

🙏

[lapis token]

I ALREADY KNEW THAT THO-

[zenith jackal]

oh

ok

[lapis token]

That was my idea earlier

I wasn’t sure about it

[zenith jackal]

yes

u got it

[lapis token]

Nor did I know how

[zenith jackal]

do you got it now @lapis token

or need to move on to next steps

[lapis token]

How about this then?

The top part is relevant to understand the transformations

[lapis token]

I feel like I might need a bit more help

[zenith jackal]

is the bottom part your notes

[lapis token]

Yes

[zenith jackal]

yes

ur right 100%

[lapis token]

That’s honestly annoying

That means I need to figure out the inverse transformation for z->x

It would’ve been much more convenient the other way around because I already had to suffer through that

[zenith jackal]

oh yeah

sometimes it makes me wish i let someone else handle this

but not many people are at this level of math

especially beyond to the point of teaching it 😭

[lapis token]

After that can I just write the transformations individually or do I need to multiply them

[lapis token]

Wdym

[zenith jackal]

means that its a lot of work to solve these questions

[lapis token]

Oh yeah

It’s terrible

[zenith jackal]

you are in a pretty complex math class

[lapis token]

I started university one month ago tho

[zenith jackal]

you must multiply them

[lapis token]

I hate it already tbh

[zenith jackal]

Its ok

[lapis token]

IM NOT EVEN STUDYING MATH THO

Anyway fine

I’ll multiply them

I need to be up in 6 hours but eh

.close

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[foggy mortar]

Hello! Can I get some help on this question? I don't really know where to start.

[zenith jackal]

Sure

[foggy mortar]

Thank you

[austere forge]

think about what f looks like when x is rational, versus x being irrational

[zenith jackal]

^

He worded it better than I couldve lol

[austere forge]

because, for irrational x, f(x) = 0

[foggy mortar]

When x is rational, x is not 0

But we don't know whether the number next to the one produced by x is rational or irrational so would the function not be continuous for rational values of x?

[austere forge]

yes, but what about irrational values of x?

[foggy mortar]

I'm not sure.

[austere forge]

for rational x, its fairly easy to see that f(x) is discontinuous because f(x) would vary wildly. for irrational x, you know f(x) = 0

[foggy mortar]

Would I have to use the delta-epsilon definition of continuity?

[austere forge]

it says you dont need to provide a proof

[foggy mortar]

Ok

[twin atlas]

That's literally the Dirichlet function in a way. If I am not mistaken it's continous for irrational numbers

[foggy mortar]

Okay, thanks. Why would it be continuous for irrational numbers though?

[austere forge]

remember what continuity is

[twin atlas]

Irrationals are dense in the reals.

A.k.a there are way way way way more irrationals and they can be very close to each other

[foggy mortar]

okay

[austere forge]

$\forall x_0 \in \mathbb{R}\setminus\mathbb{Q}, \lim_{x\to x_0} f(x) = f(x_0)$

[flat frigate]

c2b7

[foggy mortar]

Is it that the limit as f(x) approaches some point exists and is approached from both sides?

[twin atlas]

Yea

[austere forge]

if f(x) is 0 for every irrational x, its easy to see why the limits would exist, and thus why it would be continuous for irrational x

[foggy mortar]

So I do get this part but how would I know whether the function is continuous at all of the irrational numbers?

Is it because there are more irrationals?

[twin atlas]

More or less yes

[austere forge]

no, it is because the irrational are dense in the reals as he mentioned

[foggy mortar]

Okay, I think I get it now. Thank you very much!

[twin atlas]

Rational numbers are countable

Irrationals are uncountable

a.k.a way more

U can also try to solve this thing 😂 this is how we can construct the Dirichlet function I don't recommend

Smh

[austere forge]

if you think about a function f(x) = 1 for rational x, and f(x) = 0 for irrational x (dirichlet function), then it would be continous over Q and R\Q seperately, but not over R as a whole

[twin atlas]

Exactly

[foggy mortar]

Yeah I'll pass on that

Well thank you guys for your help and have a nice day!

[twin atlas]

U too

Now I will go to class have a good one

[foggy mortar]

.close

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[analog arch]

mathematical induction here, I'm confused on where did the 2 go?, I know why we added it, so we can combine the fraction but not from that onward

[median vigil]

1 + 2 = 3

[analog arch]

could you explain more

[median vigil]

3^(k+1) + 2 * 3^(k+1) = 3 * 3^(k+1)

[analog arch]

even if they are being multiplied to something else we can add like terms?

[median vigil]

,, \frac{3^{k+1}-1}{2} + \frac{2\cdot 3^{k+1}}{2} = \frac{3^{k+1}-1 + 2 \cdot 3^{k+1}}{2} = \frac{3 \cdot 3^{k+1}-1}{2}

[flat frigate]

cloud ☁

[quasi bison]

call $3^{k+1} = z$ temporarily

[flat frigate]

Ann

[analog arch]

I know this is how it goes, I've seen the solution to it but I'm just lost

[quasi bison]

$\frac{z-1}{2} + \frac{2z}{2} = \frac{z-1+2z}{2} = \frac{3z-1}{2} = \frac{3\cdot 3^{k+1}-1}{2}$

[flat frigate]

Ann

[quasi bison]

does that now make more sense to you

[analog arch]

OHH

yes thank you I get your version a lot easier

thank you for simplifying it in this way

.close

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[final knot]

Uhhh halooo, just want to continue my question.

Two ships leave the same port at the same time. One ship sails on a course of 125° at 18 knots while the other sails on a course of 230° at 24 knots. Find after 3 hours (a) the distance between the ships and (b) the bearing from the first ship to the second.

Here's my progress, I already have all sides and the angles. I'm quite lost on to how to get the bearing.

[final knot]

<@&286206848099549185>

🙏

[zenith jackal]

the bearing is not the same as the interior triangle angle.

[modern fractal]

I think you can apply cosine rule

[zenith jackal]

cos rule triples the work here

it works but triples the work

[safe radish]

@final knot Has your question been resolved?

[surreal vapor]

This is the same question as yesterday, correct @final knot ?

[safe radish]

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[final knot]

Yes, but like I got confused midway finding the bearing

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[lilac epoch]

Idk how to do this at all

Can you teach me how to?

[clever gale]

f and g are inverses

[split kayak]

dont give out answers without explanation

[split kayak]

This is more about theory anyways
Do you remember the definition of surjection and injection of functions?

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[loud cedar]

Clarification in radius do I put the number being squared of just the number like 12 or 12*2

[vagrant ice]

it's just 12

[loud cedar]

Ohh

Oki

I wanna know why

Why not squared

[vagrant ice]

if you compare back to (x - h)^2 + (y - k)^2 = r^2

that means 144 is r^2

but since the radius can't be negative

r^2 = 144 implies r = 12

[loud cedar]

okayy

Thanks

[vagrant ice]

no worries!

[loud cedar]

.close

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[zealous mason]

How to calculate

Cos-1 = 10/15

[fickle yoke]

u want $\cos^{-1}(10/15)$?

[flat frigate]

Viͥђaͣnͫ

[zealous mason]

Yes

[fickle yoke]

use calculator

idk

u can compare it with known values tho

like cos(45 degree) and cos(60 degree)

then use a linear approximation

[zealous mason]

Okay baby

Also

in order to find an angle, you need to know at LEAST one side?

[fickle yoke]

yep

[zealous mason]

Ok

And to find all sides

You need at least one angle and one side?

@fickle yoke

[fickle yoke]

yeah just not the 90 degree one

[zealous mason]

Also to work with sin, cos, tg you need a right triangle?

@fickle yoke

<@&286206848099549185>

[gritty sable]

?

[gritty sable]

Not necessarily

can apply in other triangles too!

[zealous mason]

Fine!

Thanks guys

.close

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[fickle yoke]

.at least tell him the formula is different😭

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[lilac epoch]

.reopen

Yo

[lilac epoch]

I didn’t get it?

@clever gale and @split kayak

[lilac epoch]

?

[warm warren]

kk

$f(g(x)) = x$

[flat frigate]

Annie Maqionde

[warm warren]

so have you been taught surjective, injective and bijective functions?

[lilac epoch]

Not really

[warm warren]

do you know what the domain and the range of a function is?

[lilac epoch]

Yup

[lilac epoch]

Yes

[warm warren]

k

[lilac epoch]

We have been taught

That

[warm warren]

Denote $f\circ g$ by $I$

[flat frigate]

Annie Maqionde

[warm warren]

now have you been taught what is the inverse of a function?

[lilac epoch]

Yes

[lilac epoch]

Ye

[warm warren]

so since $f\circ g$ is $I$, i.e. the identity function, by definition $g = f^{-1}$

[flat frigate]

Annie Maqionde

[warm warren]

but this holds if and only if $f$ is bijective

[flat frigate]

Annie Maqionde

[lilac epoch]

Oh okay

I got it

Thanks

.close

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[crisp maple]

not really sure what to do
thought i could maybe use mvt but i don't think that would actually do anything

[kind seal]

It follows from the epsilon delta definition of the limit I suppose

@crisp maple what have you done so far

[split kayak]

It should be easily proven through the definition of a continuous function using delta-epsilon.

well, that and the idea of a strictly increasing function in an interval

[split kayak]

well, delta-epsilon or whatever other proof method / argument you wanna invoke

[crisp maple]

uh lemme think about that then

Not sure if I'm getting at the right thing here
Not really sure how I'm supposed to get to what I want to prove

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@crisp maple Has your question been resolved?

[bright cedar]

can i help

[crisp maple]

sure

still not really sure what I'm supposed to do but its ok I'll go ask my prof at office hours later today thanks guys.

.close

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[spring saffron]

Hello, can someone give me a hint on this

[spring saffron]

x^3+30x+25=y^4 find max(x+y)

x and y are integers

[gleaming coral]

max (x + y)?

[spring saffron]

yes

[gleaming coral]

yep, sorry, have no idea

[spring saffron]

ok, np

[obsidian oracle]

Are you sure you wrote it correctly? I'm not even sure there are integer solutions

[spring saffron]

yes i wrote it correctly

i solved it, it has no solution

.close

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[obsidian tinsel]

Can someone help me on this probleme please